A demand exists in the oil and gas field for accurate models of subterranean, or subsurface, regions, such as of subsurface structures and features, fluids, properties, and/or related parameters thereof. Some of the most precise information and tools are available from full-field models, which also may be referred to as full-physics models. These models are complex, implicit, fine-scale computer simulations of the subterranean region to be modeled, and may be based on the fundamental physics of the parameter(s) to be modeled in the subterranean region. These full-physics models may be used for such illustrative purposes as to simulate and/or predict future values, performance, responses to changes in variables, etc. of the corresponding subsurface region, or portions thereof. Specific illustrative, non-exclusive examples include modeling and/or predicting hydrocarbon flow from producer wells, water flow, injectivity of a formation, well drilling, production from a well, completion of a well, and well operability limits, which may refer to the ability of a well to withstand changes in subsurface geomechanical stresses. Advances in modeling techniques have permitted improved simulation of sub-surface regions, including the physics exhibited in these regions, such as non-Darcy and multiphase flow through complicated well configurations.
Historically, these full-physics models are computationally-intensive, demanding implicit models that take significant amounts of time and resources to prepare, validate, and implement. The time required refers to the number of hours that individuals must spend to prepare, validate, and implement the model, with this time typically being performed by one or more of a relatively limited number of individuals with sufficient training and technical expertise to create these models. For example, these individuals may be highly trained individuals having expert knowledge of reservoir fluid flow mechanics, geomechanics, and mathematical modeling of dynamic bodies. In addition, the computational resources required to prepare, validate, and implement these implicit models typically require specialized software and powerful computers, including computers that can implement and solve complex finite element problems.
Understanding the behavior of subsurface regions often involves the use of numerical methods to simulate and/or analyze activities associated with the subsurface region being modeled, such as hydrocarbon recovery, fluid injection or operability limits. One such numerical method includes finite element analysis, which determines an approximate numerical solution to a complex differential equation relating to one or more parameters within the subsurface region of interest. In finite element analysis for modeling of a subsurface region, the subsurface region under study is defined by a finite number of individual sub-regions, or elements. These elements have a predetermined set of boundary conditions. Creating the elements entails gridding, or “meshing,” the subsurface region to be modeled. A mesh is a collection of elements that fills a space, with the elements being representative of a system which resides in that space. The process of dividing a subsurface region under study into elements may be referred to as “discretization” or “mesh generation” of the subsurface region.
Finite element methods also use a system of points called nodes, which may represent at least the intersections between adjacent elements of the discretized subsurface region. The elements are programmed to contain the material properties that define how the corresponding subsurface region being modeled will react to certain loading conditions. Nodes are placed at a variable density throughout the subsurface region under study. For modeling of subsurface regions, such as subsurface regions that include a reservoir, changes to the geological system are predicted as changes in parameters associated with the subsurface region, such as fluid pressures, fluid flow rates, temperatures, stresses, and the like. This means that a value for a parameter may be approximated at a particular location by determining that value within its element.
In conventional numerical studies for simulation and modeling of subsurface regions, it is important to explicitly conform to the geometrical shape of the subsurface region under analysis. This means that the elements honor the geometry of the subsurface region, including any subsurface features present in the subsurface region. In this respect, subsurface regions containing hydrocarbon reservoirs, including reservoirs under production, typically contain various forms of natural or manmade subsurface features. Illustrative, non-exclusive examples of natural subsurface features include faults, natural fractures, fluid traps, and formation stratification. Illustrative, non-exclusive examples of man-made subsurface features include a wellbore, perforations from the wellbore, man-made fractures, and wormholes, such as a result of acid injection activities. Man-made subsurface features may result from such activities as drilling, producing, injection, and completion in or near the subsurface region of interest. These subsurface features may affect reservoir behavior. As an illustrative, non-exclusive example, these subsurface features may cause steep gradients in reservoir pressure, porous flow, temperature, and/or stress.
The use of finite elements in modeling of subsurface regions is challenged by the presence of such subsurface features. Conventional numerical simulators require a grid system that honors the geometry of the subsurface region, including subsurface features therein. However, from a geometric standpoint, finite element methods generally benefit from a structured mesh as opposed to an unstructured mesh. Although meshing with an unstructured mesh may be easier than with a structured mesh, unstructured meshes are generally less accurate and can be much less efficient in how they represent the subsurface domain.
The existence of arbitrarily and/or irregularly shaped subsurface features makes it difficult to build a structured mesh. Constructing a high-quality mesh for each geometrical variation may require significant man-power, considerable expertise, and information about the variable, or physics-based, property gradients associated with such features. Failure to honor transmissible boundaries created by wormholes, fractures, stratification breaks and the like can cause simulations of subsurface regions containing these subsurface features to be inaccurate. Moreover, in simulations, or models, of the corresponding subsurface region, a greater mesh density may be necessary in such regions in order to accurately simulate and/or analyze the region, including fluid flow therein. This increase in mesh density may significantly increase the time required to create the mesh and/or the resulting full-physics model, as well as the size of such models.
Creating an accurate mesh, or discretization, of the subsurface region of interest typically represents a substantial portion of the time required to generate a full-physics model of the subsurface region, with the required creation time often being exacerbated by geometric complexities created by the interior and/or exterior complexities of subsurface features present in the subsurface regions. Moreover, prior efforts to manually generate such accurate meshes often have resulted in oversized models of the subsurface region. The difficulties resulting from which include the dramatic (often exponential) increase in time required to solve the computer model.